Statistical analysis of longitudinal data on tumour growth in mice experiments

We consider mice experiments where tumour cells are injected so that a tumour starts to grow. When the tumour reaches a certain volume, mice are randomized into treatment groups. Tumour volume is measured repeatedly until the mouse dies or is sacrificed. Tumour growth rates are compared between groups. We propose and evaluate linear regression for analysis accounting for the correlation among repeated measurements per mouse. More specifically, we examined five models with three different variance-covariance structures in order to recommend the least complex method for small to moderate sample sizes encountered in animal experiments. We performed a simulation study based on data from three previous experiments to investigate the properties of estimates of the difference between treatment groups. Models were estimated via marginal modelling using generalized least squares and restricted maximum likelihood estimation. A model with an autoregressive (AR-1) covariance structure was efficient and unbiased retaining nominal coverage and type I error when the AR-1 variance-covariance matrix correctly specified the association between repeated measurements. When the variance-covariance was misspecified, that model was still unbiased but the type I error and the coverage rates were affected depending on the degree of misspecification. A linear regression model with an autoregressive (AR-1) covariance structure is an adequate model to analyse experiments that compare tumour growth rates between treatment groups.